Abstract
The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies. The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is thus a practically and physically important problem that needs to be clearly understood. Here, we approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. Our model is described as a driven nonlinear pendulum where the motive force is the temperature difference. The rotational state and the stationary state of the engine are described as a stable limit cycle and a stable fixed point of the dynamical equations, respectively. These two states coexist under a sufficient temperature difference, whereas the stable limit cycle does not exist under a temperature difference that is too small. Using a nonlinear bifurcation analysis, we show that the disappearance of the stable limit cycle occurs via a homoclinic bifurcation, with the temperature difference being the bifurcation parameter.
Highlights
The low-temperature-differential (LTD) Stirling heat engine technology constitutes one of the important sustainable energy technologies
While a simple theoretical model of an LTD Stirling heat engine that reproduces the rotational motion of the engine has been proposed [5], how this motion is lost with decreasing temperature difference remains to be clarified
We provide an answer to this question by proposing and investigating a minimal model of an LTD Stirling heat engine based on nonlinear dynamics
Summary
The basic question of how the rotational motion of the LTD Stirling heat engine is maintained or lost based on the temperature difference is a practically and physically important problem that needs to be clearly understood. We approach this problem by proposing and investigating a minimal nonlinear dynamic model of an LTD kinematic Stirling heat engine. In contrast to the ideal Stirling thermodynamic cycle with an external operation [1, 2], actual Stirling heat engines run autonomously in a selfsustained manner under a sufficient temperature difference This is accomplished with the aid of a crank-piston mechanism [1, 2].
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